The slope of a line through two given points P1(x1,y1) and P2(x2,y2) is given by the expression:
m=(y2-y1)/(x2-x1)
Since y2=y1, so y2-y1=0.
Next we have to check if the slope exists:
(x2-x1)=1-(-1)=2 ≠ 0.
Therefore m=0/2=0.

Note: if y2=y1 and x2=x1, then P1 and P2 are two coincident points, and the slope does not exist, because we cannot define a line through two coincident points.

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